Tuesday, September 24, 2013 Independent samples t-test

Tuesday, September 24, 2013

Independent samples t-test

Exam I Results, 2013M = 77.16S = 13.30

109 18 9,9,8,8,8,7,6,5,4,4,3,1,17 9,8,6,5,46 9,8,2,254 83 8

Good work; room to improveCaution: More effort neededTrouble: Seek extra help asap

Next Homework (due Tuesday, October 1)

Chapter 10: 1-4, 6, 21, 22 Chapter 11: 1, 5, 9, 10, 18, 20

Monitor Your Understanding

http://teachertap.appspot.com/Please click on the above link, and type (or paste) where it says “classroom”:

340.01_9/24/13

Then click buttons “got it” “unsure” or “lost me” to provide anonymous feedback about your understanding throughout the lecture

http://teachertap.appspot.com/

Last TimeLast Time

• Introduction to t-tests (starting with the one-sample t-test)

• Use of sM (the estimated standard error in the denominator)

• Knowing when to use the one-sample t-test and when to use the z-score test

• Questions about these items before we move on?

Statistical analysis follows design

• The one-sample z-test can be used when:

– 1 sample– One score per subject

– Population mean (μ) and standard deviation () are known


• The one-sample t-test can be used when:

– 1 sample– One score per subject

– Population mean (μ) is known

– but standard deviation () is NOT known

Monitor your understanding

Please provide feedback on teacher tap to let me know if you understand.


Classroom: 340.01_9/24/13


Independent samples• What are we doing when we test the hypotheses?

– Consider a new variation of our memory experiment example

Memory treatment

Memory patients Memory

Test

• the memory treatment population is the same as those in the population of untreated memory patients (μA = μB).• they aren’t the same as those in the population of memory patients (μA ≠ μB)

H0

:HA:

Memory placebo

MemoryTest

Compare these two means


• The independent samples t-test can be used when:

– 2 samples

– Samples are independent

Performing your Performing your statistical teststatistical test

Test statistic

Diff. Expected by chance

Standard error

Estimated standard error

One sample z One sample t

different

Don’t know this,so need to estimate it

Degrees of freedom

Statistical Tests Summary

Design Statistical test(Estimated) Standard error

One sample, σ knownOne sample, σ unknownTwo independent samples, σ unknown

(nA – 1) + (nB -1)

Degrees of freedom

n – 1

Performing your statistical test

Estimate of the standard error based on the variability of both samples


Test statistic

One-sample tIndependent-samples t

Sample means


Test statistic


Population means• from the null hypothesis


Test statistic


Population means• from the hypotheses

H0

:Memory performance by the treatment group is equal to memory performance by the no treatment group.So:




Classroom: 340.01_9/24/13



Test statistic

One-sample t

Estimated standard error(difference expected by chance)

estimate is based on one

sample

We have two samples, so the estimate is based on two

samples




Classroom: 340.01_9/24/13



“pooled variance”

We combine the variance from the two

samples

Number of

subjects in group

A

Number of

subjects in group

B

variance


“pooled variance”

We combine the variance from the two

samples

Recall “weighted means,”

need to use “weighted

variances” hereVariance (s2) * degrees of freedom (df)


Independent-samples t• Compute your estimated standard error

• Compute your t-statistic

• Compute your degrees of freedom

This is the one you use to look up your tcrit




Classroom: 340.01_9/24/13



PersonExp. group

Control

group1

23

4

45

5540

60

43

4935

51

H0: µA = µB (µA - µB = 0)

HA: µA ≠ µB

Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he randomly assigns 8 patients to one of two samples. He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a memory test. The data are presented below. Use α = 0.05.

α = 0.052-tailed test


PersonExp. group

Control

group1

23

4

45

5540

60

43

4935

51

Need to compute the mean and variability for each sample


H0: µA = µB (µA - µB = 0); HA: µA ≠ µB; α = 0.05; 2-tailed


PersonExp. group

Control

group1

23

4

45

5540

60

43

4935

51

Need to compute the mean and variability for each sampleControl group

= 50

(45-50)2 + (55-50)2 + (40-50)2 + (60-50)2

= 250

SS =A


H0: µtreatment = µcontrol HA: µtreatment ≠ µcontrol, α = 0.05 2-tailed


Exp. group

(43-44.5)2 + (49- 44.5)2 + (35- 44.5)2 + (51- 44.5)2

= 155

SS =B

PersonExp. group

Control

group1

23

4

45

5540

60

43

4935

51

Need to compute the mean and variability for each sample


= 44.5



PersonExp. group

Control

group1

23

4

45

5540

60

43

4935

51


= 0.95



Tobs= 0.95Tcrit= ±2.447α =

0.05Two-tailed

PersonExp. group

Control

group1

23

4

45

5540

60

43

4935

51


= 0.95


Tobs= 0.95α = 0.05

Two-tailedTcrit= ±2.447

PersonExp. group

Control

group1

23

4

45

5540

60

43

4935

51


+2.45 = tcrit

- Fail to Reject H0

tobs=0.95

= 0.95


Tobs= 0.95α = 0.05

Two-tailedTcrit= ±2.447

Tobs Tcrit

Compare<

Fail to reject the H0 and conclude that A= B

PersonExp. group

Control

group1

23

4

45

5540

60

43

4935

51

Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he randomly assigns 8 patients to one of two samples. He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a memory test. The data are presented below. Use α= 0.05.

= 0.95




Classroom: 340.01_9/24/13


Assumptions of the independent samples t-test

• Each of the population distributions follows a normal curve (but test is robust to violations of this assumption if the sample is large)

• The two populations have the same variance• If the variance is not equal and the samples

are very different in size, use the corrected degrees of freedom provided after Levene’s test (see spss output)

Practice problemYou are conducting an experiment about methods for

teaching reading. You have access to a sample of 10 3rd graders. You randomly assign half of the group to an experimental reading intervention, and the other half receives instruction as usual in their classrooms. After the intervention, you measure the number of words each child can read correctly in one minute, and obtain the following results.

• Group 1 (experimental) scores: 30, 35, 40, 20, 32• Group 2 scores: 25, 30, 20, 18, 18• Conduct a t-test to find out whether the groups

are different in reading ability at the end of the study.

• t table

http://mips.stanford.edu/public/classes/stats_data_analysis/principles/t_table.html

Using spss to conduct t-tests

• One-sample t-test: Analyze =>Compare Means =>One sample t-test. Select the variable you want to analyze, and type in the expected mean based on your null hypothesis.

• Independent samples t-test: Analyze =>Compare Means =>Independent samples t-test. Specify test variable and grouping variable, and click on define groups to specify how grouping variable will identify groups.

Practice problem

Use SPSS to conduct a one-sample t-test to see if the students in this class are taller than the average college student (μ= 66.5 inches).

Use SPSS to conduct an independent samples t-test comparing the heights of men and women, based on the data from this class.

Using excel to compute t-tests

• =t-test(array1,array2,tails,type)• Select the arrays that you want to

compare, specify number of tails (1 or 2) and type of t-test (1=dependent, 2=independent w/equal variance assumed, 3=independent w/unequal variance assumed).

• Returns the p-value associated with the t-test.

Effect Size for the t Test for Independent Means

• Estimated effect size after a completed study

Power for the t Test for Independent Means (.05 significance level)

Approximate Sample Size Needed for 80% Power (.05 significance

level)

Next Homework (due Tuesday, October 1)

Chapter 10: 1-4, 6, 21, 22 Chapter 11: 1, 5, 9, 10, 18, 20

Documents

Tuesday, September 24, 2013 Independent samples t-test